10c Appendix 1. Hydrated salts, metal-aqua complex ions and their relative acidity

(not necessarily just transition metal ions)

• All metal ions in solution are 'associated' with water. The water molecules can also be weakly bonded or more strongly as a ligand to form a complex ion, and these can also present in solid 'hydrated' salts on crystallisation e.g.

  • FeSO₄.7H₂O_(s), CoCl₂.6H₂O_(s), CuSO₄.5H₂O_(s) etc.

    • Iron(II) sulphate heptahydrate, cobalt(II) chloride hexahydrate and copper(II) sulphate pentahydrate.

    • The above crystals contain 7, 6 and 5 molecules of water of crystallisation respectively.

    • A hexa-aqua ion is present in the first two, [M(H₂O₆)]²⁺ (M = Fe, Co)

  • In the case of copper(II) sulphate, 4 water molecules are covalently bonded to form a square planar complex ion, [Cu(H₂O)₄]²⁺ and the 5th water molecule is hydrogen bonded to this ion and a neighbouring sulphate ion helping to hold the crystal lattice together.

    • However, this blue crystal lattice is readily broken down on heating, a classical demonstration of a reversible reaction, since the white anhydrous solid turns blue on adding water (a simple test for water.

    • CuSO₄.5H₂O_(s) CuSO_4(s) + 5H₂O_(g/l)

• Lewis acid-base theory:

  • A base is an electron pair donor and an acid is an electron pair acceptor.

  • Ligands like water, can donate a pair of non-bonding electrons (lone pair) into a vacant orbital of a central metal ion and so dative covalent (co-ordinate) bonds hold a complex together.

  • The central metal ion with vacant bonding orbitals can act as a Lewis acid.

  • Ligands act as Lewis bases by electron pair donation to form the metal-ligand bond.

• Bronsted-Lowry acid-base theory (essentially a sub-set of Lewis Theory)

  • A base is a proton acceptor.

    • This is via an electron lone pair on the base (a Lewis base is a lone pair donor).

    • e.g.

  • An acid is proton donor.

    • This involves a heterolytic breakage of an X-H bond (a Lewis acid is an electron pair acceptor).

    • e.g.

• Many hexa-aqa complex ions can undergo acid-base reactions with water to produce solutions of pH less than 7.

  • Usually group 2, 3 and transition metal ions.

  • The positive central metal ion polarises a water molecule, releasing a proton, H⁺.

  • In the deprotonation reaction the proton transfers to water and the overall charge on the complex falls by 1 unit since the H₂O - H⁺ = OH^-, i.e. one of the ligands is now a hydroxide ion.

  • In these reactions the hydrated ions act as Bronsted Lowry acids and water acts as a Bronsted-Lowry base.

• e.g. [M(H₂O)₆]²⁺_(aq) + H₂O_(l) [M(H₂O)₅(OH)]⁺_(aq) + H₃O⁺_(aq) 

  • e.g. when M = Mn, Fe, Co, Ni, Cu, Mg etc. give very weak acid solutions with pH's just less than 7.

    • Ti(II), V(II) and Cr(II) M²⁺ ions are redox unstable in the presence of air, but theoretically their salts give very weakly  acid solutions, but, since they are usually prepared by zinc-acid reduction from higher oxidation states, its not a very relevant fact here.

• e.g. [M(H₂O)₆]³⁺_(aq) + H₂O_(l) [M(H₂O)₅(OH)]²⁺_(aq) + H₃O⁺_(aq) 

  • e.g. when M = Ti, V, Cr, Fe, Al etc. give very weak acids solutions (but generally stronger than for M²⁺) of pH's in the 3-5 region.

  • In the presence of alkali, OH^-, removing H₃O⁺ ions, the  equilibrium moves more to the right and more protons are lost from the complex in stages until the hydroxide precipitate is formed e.g. for iron(III), chromium(III) or aluminium.

    • [M(H₂O)₆]³⁺_(aq) + 3OH^-_(aq) [M(H₂O)₃(OH)₃]⁰_(aq) + 3H₂O_(l) 

  • Some of the M³⁺ hydroxides are amphoteric and dissolve in excess alkali (1.) or acid (2.) e.g. to eventually form for iron(III) or aluminium, 1. the soluble hexa-hydroxo complex ion or 2. the original hexa-aqua ion.

    1. [M(H₂O)₃(OH)₃]⁰_(aq) + 3OH^-_(aq)  [M(OH)₆]^3-_(aq)+ 3H₂O_(l) 

    2. [M(H₂O)₃(OH)₃]⁰_(aq) + 3H₃O⁺_(aq)  [M(H₂O)₆]³⁺_(aq) + 3H₂O_(l)

• As a general rule the greater the polarising power of the central metal ion, the lower the pH of the resulting aqueous solution, i.e. the acid-base equilibrium is shifted more to the right causing an increase in acidity of the solution.

  • This effect and process facilitated by the central metal ion on one water ligand molecule can be envisaged as

    • [M-O-H₂]ⁿ⁺ ==> [M-O-H]^n+-1 + H⁺ (proton transferred to a water molecule)

    • One of the O-H bond pairs is 'attracted' onto the oxygen atom by the electric field effect of the central metal ion of charge n+, allowing proton transfer to the base water.

  • Polarising power is a function of ionic charge/ionic radius ratio. therefore ...

    • the greater the metal ion charge (n+), the more acidic the solution,

    • and the smaller the radius of the metal ion, the more acidic the solution, so ...

  • both increasing charge, or decreasing the central cation radius intensify the electric field polarising effect on a water ligand.

• The acidity of the hexaaquions M³⁺_(aq) due to the polarising influence of the central highly charged M³⁺ ion accounts for the lack of stability/existence of e.g. aluminium carbonate, iron(III) carbonate or chromium(III) carbonate, whereas MgCO₃ , ZnCO₃ and FeCO₃ etc. with the less polarising M²⁺ ion exist. It also accounts for why you see bubbles of carbon dioxide when carbonates/hydrogencarbonates are mixed with aluminium chloride, iron(III) chloride or chromium(III) chloride solutions e.g.

  • 2[Fe(H₂O)₆]³⁺_(aq) + CO₃^2-_(aq) 2[Fe(H₂O)₅(OH)]²⁺_(aq) + H₂O_(l) + CO_2(g)   

  • or [M(H₂O)₆]³⁺_(aq) + HCO₃^-_(aq) [M(H₂O)₅(OH)]²⁺_(aq) + H₂O_(l) + CO_2(g)

  • There several legitimate permutations based on these equations.

• -

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 2. Complexes - introduction: ligands, bonding, co-ordination number and charge on complex ions

• A complex is formed by the combination of a central metal ion surrounded by, and bonded to, neutral molecules or ions acting as 'ligands' (bits stuck on or appendages).

  • If you have already read Appendix 1. you should note that it is riddled with complex ions and the central metal ion does NOT have to be a transition element. The two ligands involved were H₂O and OH^-.

• A ligand is an atom, ion or molecule which can act as an electron pair donor (Lewis base) and usually forms a dative covalent or 'co-ordinate' bond with the central metal ion.

  • The lone pair donation is usually from an O, N or halogen atom of the ligand in this covalent co-ordinate bonding.

  • The central metal ion acts as a Lewis Acid, that is, an electron pair acceptor from the ligand by way of vacant 3d, 4s, 4p  and even 4d orbitals for the 3d-block transition elements.

  • The ligand acts as a Lewis Base, that is, an electron pair donor e.g. neutral ligands like H₂O: (water, aqua in complex name) or :NH₃ (ammonia, ammine in complex name) and negatively charged ligands like :OH^- (hydroxide, hydroxo in complex name), Cl^- (chloride ion, chloro in complex name) and :CN^- (cyanide ion, cyano in complex name).

  • ...

    • A an example of the bonding in a complex ion is shown in the above diagram. The negative cyanide ion is a monodentate ligand (forms one bond per ligand) and donates an electron pair into a vacant 3d, 4s or 4p orbital in the iron(III) ion to form six dative covalent bonds.

    • The resulting ion has the formula [Fe(CN)₆]^3-, the overall charge of 3- is the aggregate of 6- (cyanide ions) plus 3+ (iron ion)

    • The co-ordination number of 6, which means there are 6 central metal ion - ligand bonds. It doesn't necessarily mean six ligands, you can get a co-ordination number of 6 from three co-ordinated bidentate ligands (2 bonds per ligand), two tridentate ligands and from EDTA just one ligand can form 6 dative covalent bonds with a central metal ion. More on this below.

• The ligand may attach itself by one or more bonds. The suffix '...dentate', prefixed by mono/uni/bi/ploy/multi e.g. monodentate (unidentate), bidentate, or polydentate (multidentate) is used to denote the number of bonds each ligand makes with the central metal ion.

• The total number of ligand bonds to the central metal ion is called the co-ordination number.

  • It is not the number of ligands, unless it is a monodentate ligand.

  • There is no firm rules relating shape to a particular ligand.

  • The six ligands don't have to be the same e.g. ...

    • ... which is the dichlorotetraaquachromium(III) ion. This octahedral complex with a co-ordination number of 6, and note this has an overall ion charge of (2 x - from 2Cl^-) + (3+ from Cr³⁺) = +, water is an electrically neutral ligand.

      • ... and in equations the complex ion would be written as [Cr(H₂O)₄Cl₂]⁺

• Examples of unidentate/monodentate ligands:

  • e.g. neutral ligands: water H₂O:, ammonia :NH₃, primary aliphatic amines e.g. butylamine CH₃CH₂CH₂CH₂NH₂, 

  • These ligands often form octahedralshaped complexes with a co-ordination number of 6.

  • e.g. negative ligands: chloride Cl^-, cyanide CN^-,

  • The chloride ion Cl^- forms the tetrahedrale.g. the tetrachlorocuprate(II) complex ion ...

  • [CuCl₄]^2-, note the overall charge is (2+) + (4 x -) = 2- and the co-ordination number is 4.

  • The chloride ion can be too bulky to form an octahedral complex, though there is no firm rules relating shape to ligand.

  • and CN^- square planare.g. the tetracyanonickelate(II) complex ion ...

  • [Ni(CN)₄]^2-, note the overall charge is (2+) + (4 x -) = 2- and the co-ordination number is 4.

    • Note that [Cu(H₂O)₄]²⁺, the tetraaquacopper(II) ion, with the less bulky water molecule ligand, forms a blue square planar complex, whereas with the larger chloride ion, a tetrahedral complex is formed.

  • A linearshaped complex is formed between a silver ion and ammonia.

  • [Ag(NH₃)₂]⁺ is formed in 'ammoniacal' silver nitrate solution used in the test for aldehydes. The diamminesilver(I) ion has co-ordination number of 2 and an overall charge of a single + because the ammonia molecule is an electrically neutral ligand.

• Examples of bidentate ('two toothed') ligands:

  • neutral ligands: diamines like 1,2-diaminoethane (ethane-1,2-diamine) H₂NCH₂CH₂NH₂ (bonds via lone pair :N).

  • negative ligands: ethanedioate ion C₂O₄^2-, (bonds via lone pair on the :O^-). The L represents where the dative covalent bond forms.

  • shows three bidentate ligands co-ordinated to a central metal ion (co-ordination number 6, 'octahedral' in bond arrangement).

  • Examples: [Cr(H₂NCH₂CH₂NH₂)₃]³⁺, H₂NCH₂CH₂NH₂ is often represented in shorthand by en,

    • and the complex simply written as [Cr(en)₃]³⁺.

  • Bidentate ligands are the first of what are called polydentate ligands and such complexes are sometimes called chelates from the Greek for 'crab's claw' and the complex formation described as a chelation process.

• More examples of multi/polydentate ligands:

  • EDTA^4- (old name 'EthyleneDiamineTetraAcetic acid') forms six bonds with a central metal ion.

    • more details to add

  • The haemoglobin molecule acts as a multi/polydentate ligand with iron(II) ions in blood chemistry.

    • more details to add

• One ligand can replace another depending on the relative bond strengths in a reaction called ligand exchange reaction.

• When a bidentate or polydentate ligand is added to a pre-existing complex of monodentate ligands, it is highly likely a more stable complex will be formed.

  • The principal reason for this, (ignoring bond strengths), is the positive entropy change accompanying the 'release' of 4 or 6 small molecules which offer a greater variation of ways of arranging the particles or energy distribution.

• If the ligands are easily exchanged, the complex is described as 'unstable' and if the ligands are more strongly bound, the complex would be described as stable.

• Complex ion stability is also related to the oxidation state of the transition metal in the presence of a particular ligand.

• See Appendix 3. for more on complex ion shape and isomerism.

• See Appendix 5. for more on electrode potentials, oxidation state and complex ion stability.

• See Appendix 8. for more on complex ion stability, entropy changes and stability equilibrium constants (K_stab).

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 3. Complexes: more on shapes and isomerism

• Valence shell electron pair repulsion theory (VSEPR) can quite often be used to predict the shape of a complex, which is usually one of four shapes (at least at pre-university level):

• 

• Principal shapes:

  • Examples have been described in Appendix 2

  • For isomerism analysis it crucial to the think of the orientation of the bonds and not the number of ligands.

  • Octahedral (co-ordination number 6): very common, geometrical and optical isomerism possible.

    • Examples

  • Tetrahedral (co-ordination number 4): with more bulky ligands like chloride ion, optical isomerism possible.

  • Square planar (co-ordination number 4): geometrical isomerism possible.

  • Linear (co-ordination number 6): relatively rare and can't form isomers

• 

• Principal forms of isomerism:

  • Geometrical isomerism:

    • Examples of (1) above:

      • cis and trans [Pt(NH₃)₂Cl₂],

    • Examples of (2) above:

      • cis and trans [Cr(NH₃)4Cl₂]⁺,

  • Optical isomerism: Examples of (3) above.

    • (iv) [Cr(H₂NCH₂CH₂NH₂)₃]³⁺, H₂NCH₂CH₂NH₂, ethane-1,2-diamine (ethylenediamine), is often represented in shorthand by en,

      • and the complex simply written as [Cr(en)₃]³⁺.

      • This complex has mirror image forms i.e. enantiomers of optical isomers.

        • This optical isomerism can be illustrated thus

        •  where L-L represents H₂NCH₂CH₂NH₂

        • The ligand bonds via the lone pairs of electrons on the nitrogen which are donated to form the metal-ligand dative covalent bonds.

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 4. Electron configurations and the theory and variation of complex ion colour

• For the 3d-block know the complete order of filling of the sub-shells from Z=21 to 30 and be able to write out the full or abbreviated electron configuration.

  • See under each element and even more detail in Electron Configurations in Periodic Table section 2.2.

  • The number of orbitals per sub-shell, 1 for s, 3 for p, and 5 for d sub-shell.

  • PLEASE watch out for the two ‘quirks’ for Cr and Cu atoms and the order of electron removal when forming positive ions e.g. for the 3d block of transition metals, you remove the 4s electrons first, before any of the 3d electrons.

  • The idea of atomic orbitals as the space/shape of a particular electronic level or sub-shell helps ion this section.

• Transition metals can be identified by the colour of their complexes which of course is a very characteristic feature of their chemistry (e.g. the hydroxide precipitates which are, of course, all neutral complexes).

• The colour can varies with change in (i) oxidation state, (ii) ligand and (iii) co-ordination number or shape (which in turn depends on the ligand and oxidation sate).

• All of these three factors are linked to the electronic state of the central metal ion, so, if the electronic levels are changed, the difference between quantum levels changes, therefore the wavelength of the light photons absorbed changes, i.e. the observed colour changes e.g.

  • e.g. (i) The same ligand (H₂O), shape and co-ordination number but different oxidation state.

    • [Fe(H₂O)₆]²⁺, pale green iron(II) ion and [Fe(H₂O)₆]³⁺, yellow-brown iron(III) ion.

      • Oxidation states +2 and +3, both octahedral complexes with co-ordination number 6.

  • e.g. (ii) The same oxidation state, shape and co-ordination number but different ligand.

    • [Ni(H₂O)₆]²⁺, green hexaaquanickel(II) ion and [Ni(NH₃)₆]²⁺, pale blue hexaamminenickel(II) ion.

      • Both oxidation state +2, both octahedral complexes with co-ordination number 6, but different ligands i.e. water and ammonia.

  • e.g. (iii) The same oxidation state but with a different ligand, shape and co-ordination number.

    • [Cu(H₂O)₆]²⁺, blue hexaaquacopper(II) ion and [CuCl₄]^2-, yellow tetrachlorocuprate(II) ion.

    • Same oxidation state +2, but different ligands (water and chloride ion), different shape (octahedral and tetrahedral) and different co-ordination number (6 and 4).

• COLOUR THEORY for transition element complexes: The argument is presented from the point of view of an octahedral complex, but similar arguments apply for a tetrahedral or square planar complex.

• There are five 3d sub-shell orbitals whose 3D spatial representations are shown below. Theoretically it is considered that the ligands in an octahedral complex approach the central metal ion along the x, y and z axis, which would minimise the repulsion between the orbitals of bonding electrons in the six M-ligand dative covalent bonds (note that 4s and 4p orbitals are involved in complex ion bonding).

  • The d orbitals point either along or between the x,y,z Cartesian axes.

• The approach and bonding of these ligands raises the energy of all of the 3d orbitals, but not all equally so.

  • For an octahedral complex, the two orbitals lying on the x, y and z axes (4) and (5) experience more repulsion than the other three orbitals lying between the x, y and z axes (1), (2) and (3) when the six co-ordinate covalent ligand - metal ion bonds are formed.

  • This unequal ligand repulsion causes a splitting in the 3d orbital quantum levels.

  • In each of the four box diagrams (1)-(4) below, the five raised 3d 'degenerate' (meaning equal) orbitals are shown on the left, and the 'splitting' effect of the ligands is shown on the right.

  • The lower three 3d orbitals represent the 'new' ground state.

  • The upper two 3d orbitals represent either an upper ground state if the lower 3d levels are fully occupied, or more pertinent to colour theory, a potentially upper excited state if they are not fully occupied.

  • We can now consider what possible electronic 'transitions' can take place for four different ions - coloured and colourless.

The electronically excited states of titanium(III) and copper(II) are illustrated below.

• The colour arises from electronic transitions from the ground state to excited states, the energy needed can be calculated using

  • Planck's Equation, ΔE = hv , E = energy of a single photon (J), h =  Planck's Constant (6.63 x 10-34 JHz^-1), v = frequency (Hz).

  • Therefore if the photo energy/frequency is equal to ΔE  then energy is absorbed and an electron can be promoted from the lower 3d level to the higher 3d level.

  • If ΔE is in the visible light frequency range the complex will be 'coloured'.

  • In the case of coloured transition metal complexes, the colour arises from visible light energy absorption on promoting electrons from the lower 3d levels to the higher 3d levels.

• However, this can only occur if there is at least one electron in the 'lower' 3d orbitals and at least one half-filled 'higher' 3d quantum level, i.e. the minimum pre-conditions for an electronic transition or 'excitation'.

• Consequently because there a lack of such possible transitions in Sc(III) and Zn(II) their compounds are usually colourless i.e. no light absorbed in the visible region of the spectrum

• In the true transition metals from Ti to Cu, it is possible for the electromagnetic radiation energy to produce this excitation from the lower to the higher 3d sub-levels and it is usually in the visible region. The frequencies of visible radiation are absorbed and the perceived colour arises from the frequencies not absorbed.

• The electronic structure and colour of some typical 'simple' aqueous ions is shown below. They are all hexa-aqua ions of an octahedral shape except ...

  • copper(I) cannot form a stable simple Cu⁺_(aq) ion and

  • copper(II) also forms the blue square planar [Cu(H₂O)₄]²⁺ ion.

• The colour you see in a transition metal compound is the visible light that isn't absorbed by the 3d electronic transitions. For example, copper(II) complexes often absorb in the red area of the visible spectrum, so the resulting colour observed is green-blue.

• Colour changes in transition metal reactions can arise from change of ligand, change in co-ordination number or change in metal oxidation state (sometimes several of these simultaneously, see cobalt(II) ion reactions with ammonia + oxygen or chloride ion).

• The colours are quite useful for simple transition metal ion identification tests e.g. precipitates with sodium hydroxide and ammonia (see pictures) and the thiocyanate test for iron(III) ions.

• Ultraviolet and visible absorption spectra

  • ?

  • x-ref complimentary colour table in Appendix 8. Colorimetry - be able to suggest colour

  • need visible spectra pictures

• Dyes and pigments

  • Monastral blue

  • other porphyrin complexes for dyes in paint

• Ultraviolet and visible spectroscopy can be used to determine the concentration of metal ions in solution, usually after the addition of a suitable ligand to intensify the colour using the more elaborate technique of spectrophotometry or the simpler technique of colorimetry - appendix 9.

  • Theory: diagram, spectra

  • Examples:

• Colorimetric analysis of coloured solutions for quantitative analysis using a colorimeter is described in Appendix 9.

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 5. E^ø Half-cell potentials/reactions, full redox equations and calculating feasibility via E^ø_reaction

Database of Standard Electrode Potentials, E^ø values

See also the electrode potential chart

• For those mentioned on this web page for aqueous systems under standard conditions,

• i.e. at 298K, 1 mol dm^-3 concentration _(aq), 1 atm. reactant gas pressure (if appropriate),

• and compared with the half-cell potential for the standard hydrogen gas-hydrogen ion electrode (via Pt electrode interface),

  • which is assigned the arbitrary convention value of E^ø_H+(aq)/H2(g) = 0.00 V

    • 2H⁺ _(aq) + 2e^-  H_{2 (g)} 

  • Details on Part 7. Equilibria - Redox systems (opens in new window)

  • Half-cell electrode potential equations are usually quoted as a reduction (as above and list below)

• The half-cell potentials are listed downwards from the strongest reducing agent system (most negative E^ø/V) to the strongest oxidising agent system (the most positive E^ø/V):

  • ?

  • -0.76 for Zn²⁺_(aq) + 2e^- Zn_(s)  [Zn(II) ==> Zn(0)]

  • -0.56 for Fe(OH)_3(s) + e^- Fe(OH)_2(s) + OH^-_(aq)  [Fe(III) ==> Fe(II), in alkali]

  • -0.44 for Fe²⁺_(aq) + 2e^- Fe_(s)  [Fe(II) ==> Fe(0)]

  • -0.41 for Cr³⁺_(aq) + e^- Cr²⁺_(aq)  [Cr(III) ==> Cr(II), in acid]

  • -0.26 for V³⁺_(aq) + e^- V²⁺_(aq)  [V(III) ==> V(II), in acid]

  • -0.10 for [Co(NH₃)₆]³⁺_(aq) + e^- [Co(NH₃)₆]²⁺_(aq)   [Co(III) ==> Co(II) for NH₃ ligand]

  • 0.00 for 2H⁺_(aq) + 2e^-  H_2(g)  [the arbitrary assumed standard value, H(+1) ==> (H(0)]

  • +0.34 for VO²⁺_(aq) + 2H⁺_(aq) + 2e^- V³⁺_(aq) + H₂O_(l)  [V(IV) ==> V(III)]

  • +0.40 for ¹/₂O_2(g) + H₂O_(l) + 2e^-  2OH^-_(aq)  [O(0) ==> O(-2), in alkali]

  • +0.54 for I_2(aq) + 2e^- 2I^-_(aq)  [I(0) ==> I(-1)]

  • +0.77 for Fe³⁺_(aq) + e^- Fe²⁺_(aq)  [Fe(III) ==> Fe(II), in acid]

  • +1.00 for VO₂⁺_(aq) + 2H⁺_(aq) + 2e^- VO²⁺_(aq) + H₂O_(l)  [V(V) ==> V(IV) in acid]

  • +1.23 for ¹/₂O_2(g) + 2H⁺_(aq) + 2e^-   H₂O_(l)  [O(0) ==> O(-2), in acid???]

  • +1.33 for Cr₂O₇^2-_(aq) + 14H⁺_(aq) + 6e^- 2Cr³⁺_(aq) + 7H₂O_(l)  [Cr(VI) ==> Cr(III)]

  • +1.36 for Cl_2(aq) + 2e^- 2Cl^-_(aq)  [Cl(0) ==> Cl(-1)]

  • +1.51 for MnO₄^-_(aq) + 8H⁺_(aq) + 5e^- Mn²⁺_(aq) + 4H₂O_(l)  [Mn(VII) ==> Mn(II)]

  • +1.52 for Mn³⁺_(aq) + e^- Mn²⁺_(aq) + H₂O_(l)  [Mn(III) ==> Mn(II)]

  • +1.77 for H₂O_2(aq) +  2H⁺_(aq) + 2e^- 2H₂O_(l)  [O(-1) ==> O(-2), in acid?]

  • +1.82 for Co³⁺_(aq) + e^- Co²⁺_(aq)  [Co(III) ==> Co(II) for H₂O ligand]

  • +2.01 for S₂O₈^2-_(aq) + 2e^- 2SO₄^2-_(aq)  [2O(-1) ==> 2O(-2)]

  • ?

Calculation of E^ø for a redox reaction

• In principle, any accurately known half-cell potential can be used in a cell system to obtain an unknown half-cell potential which can be used to theoretically predict the feasibility of a reaction.

• The electrochemical series and electrode potential charts, know how to construct, read and use them.

• Other half-cells, they don’t have to simple metal/ metal ions, all you need is two interchangeable oxidation states eg Cl_2(aq)/Cl^-_(aq) or Mn²⁺_(aq)/MnO₄^-_(aq) etc. but both components of the half-cell must be in the same solution and in contact with a platinum electrode that connects to the rest of the circuit (Fig 12 p213).

• One way of working out E^ø values: E^ø_cell =  E^ø_(red) – E^ø_(ox)  (amounts to the difference between the half-cell potentials on an electrode potential chart)

  • * E^ø_(red) is the most positive or the least negative = the strongest oxidising agent or electron acceptor of the two half-cell systems, and the +ve battery pole, eg Cu²⁺ compared to Zn²⁺, so Cu²⁺_(aq) + 2e^- ==> Cu_(s), rather than reduction of Zn²⁺,

  • and E^ø_(ox) is the least positive or the most negative = the strongest reducing agent or electron donor of the two half-cell potentials, and the -ve battery pole eg Zn compared to Cu, so Zn_(s) - 2e^- ==> Zn²⁺_(aq) happens rather than oxidation of Cu,

  • overall cell redox reaction: Cu²⁺_(aq) + Zn_(s) ==> Cu_(s) +Zn²⁺_(aq)  

  • Calculating the voltage-Emf for the copper-zinc cell: 

    • E^ø_(red) = E^ø_{Cu(s)/Cu2+(aq)} = +0.34V, E^ø_(ox) = E^ø_{Zn(s)/Zn2+(aq)} = -0.76V

    • E^ø_cell =  E^ø_(red) – E^ø_(ox)= +0.34V - (-0.76) = + 1.10 V (feasible!)

For more details and examples see

Equilibrium Part 7 Redox equilibria, half-cell electrode potentials, electrolysis and electrochemical series

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 6. Catalysis theory and practice

• A catalyst is a substance that alters the rate of chemical reaction without itself being permanently chemically changed.

• It will chemically change temporarily e.g. change in ligand or oxidation state or other bonding arrangement, but will return to is original state often via a 2-3 stage 'catalytic cycle'.

• A catalyst provides a reaction pathway with a lower activation energy E_a, compared to the uncatalysed reaction (see diagrams immediately below, simple exothermic/endothermic reaction and more realistically, a complex two stage cycle profile further on).

Two primary modes of catalytic action - heterogeneous and homogeneous

• HETEROGENEOUS CATALYSIS: (e.g. diagram above for nickel catalysing the hydrogenation of an alkene)

  • The catalyst and reactants are in different phases (usually solid catalyst and gaseous/liquid reactants).

  • The reaction occurs on the catalyst surface which may be the transition metal or one of its compounds e.g. an oxide.

  • The reactants must be adsorbed onto the catalyst surface at the 'active sites'.

  • This can be physical adsorption or chemically bonding to the catalyst surface. Either way, it has the effect of concentrating the reactants close to each other and weakening the original intra-molecular bonds of the reactant molecules.

  • The diagram above illustrates a typical heterogeneous catalysis e.g. hydrogenation of alkenes with hydrogen and a nickel catalyst.

  • The strength of adsorption is crucial to having a 'fruitful' catalyst surface.

    • If adsorption too strong, the reactant/product molecules are too strongly 'chemisorped' inhibiting reaction progress e.g. can happen with tungsten (W).

    • If adsorption too weak, the reactants are not chemisorped strongly enough to allow the initial bond breaking processes to happen e.g. can happen with silver (Ag), though silver is used in some industrial processes.

    • Just right: Nickel (Ni), platinum (Pt), rhodium (Rh) etc. will adsorb the reactants sufficiently to enable the bond breaking process to be initiated but to not strong to retain the product molecules. These three metals are used in many industrial processes e.g. hydrogenating oils to make margarine (Ni) and catalytic converters in vehicle exhausts (Pt, Rh).

  • It is usual to use the catalyst in a finely divided form to maximise surface area to give the greatest and therefore most efficient rate of reaction. This means the catalyst must be physically supported. since it will have no bulk strength in its own right e.g.

    • Platinum-rhodium metal is produced on a temperature resistant ceramic support in catalytic converters of motor vehicle exhausts.

  • Catalyst poisoning should be avoided. This inhibiting effect is caused by impurity molecules being strongly chemisorbed on the most active sites of the catalyst surface. It considerably reduces the efficiency of the catalyst and increases production costs if the catalyst has to be replaced or functions with less efficiency e.g.

    • sulphur poisons the iron catalyst in the Haber Process for making ammonia,

    • and lead poisons the platinum-rhodium surface in car exhaust catalytic converters.

  • -

• A two stage reaction profile for a catalytic cycle (E_a = activation energy)

  • This sort of diagram is most applicable to homogeneous catalysis where definite intermediates are formed, but in general principle it applies to heterogeneous catalysis too where the adsorption (particularly chemical) is equivalent to forming a transition state or complex.

  • E_a1 is the activation energy leading to the formation of an intermediate complex.

  • E_a2 is the activation energy for the change of the intermediate complex into products.

  • E_a3 is the activation energy of the uncatalysed reaction.

• HOMOGENEOUS CATALYSIS:

  • The catalyst and reactants are in the same phase (usually a solution), and so the catalysed reaction can happen throughout the bulk of the reaction medium.

  • The catalysis is usually due to temporary changes in oxidation state of a transition metal ion and results in a 'catalytic cycle'. In other words, the homogeneous catalysed reactions occur via some intermediate species.

    • e.g. (i) Either iron(II) Fe²⁺ ions or iron(III) Fe³⁺ ions catalyse the oxidation of iodide ions by peroxodisulphate

      • uncatalysed (E_a3 in diagram above) the overall reaction is:

      • (i) S₂O₈^2- _(aq) + 2I^- _(aq) ==> 2SO₄^2- _(aq) + I_{2 (aq)} 

        • [E^ø = ]

      • However, this 'direct' uncatalysed reaction involves the collision of two repelling negative ions and so has a high activation energy. Activation energies arise from outer electron shell repulsions and bond energies.

      • BUT, the collision of an Fe³⁺ ion and an I^- ion involves positive-negative attraction which helps overcome the repulsion component activation energy due to two negative ions colliding.

      • so initially for catalysed (E_a1 in diagram above)

        • (ii) 2Fe³⁺_(aq) + 2I^-_(aq) ==> 2Fe²⁺_(aq) + I_2(aq) 

          • E^ø_reaction = V, several steps?

          • Note: If no iron(III) ions are present, but an iron(II) salt is added, iron(III) ions are generated via equation (iii) and so the catalytic cycle of reactions (ii) and (iii) can begin.

      • followed by (E_a2 in diagram above)

        • (iii) 2Fe²⁺_(aq) + S₂O₈^2-_(aq) ==> 2SO₄^2-_(aq) + 2Fe³⁺_(aq) 

          • E^ø_reaction = V, several steps

      • The iron(III) ion is regenerated in the cycle whether you start with Fe²⁺ or Fe³⁺ , showing the iron ions act in a genuine catalytic way and the iron ions are not consumed overall in the process.

      • If you added up the two equations of the cycle you get the equation of overall reaction change.

      • This is an excellent example of why transition element compounds can act as catalysts in specific redox reactions i.e. they can exist in, and interchange between, two (or more) oxidation states that facilitate the overall reaction.

      • Note 3: E^ø arguments can be used to check on the feasibility of the reaction or mechanism steps.

    • (ii) The autocatalysis by Mn²⁺ ions when the oxidising agent potassium manganate(VII), KMnO₄, is used to titrate the ethanedioate ion, C₂O₄^2-, (from acid/salt, old name 'oxalic/oxalate').

      • 2MnO₄^-_(aq) + 16H⁺_(aq)  + 5C₂O₄^2-_(aq) ==> 2Mn²⁺_(aq) + 8H₂O_(l) + 10CO_2(g) 

      • Initially, the reactant collisions are between two anions which will have a high activation energy, hence the slow start to the reaction. In the titration you see it gradually gets faster and faster because there is catalytic cycle involving the hexa-aqua Mn(II) ion and ethanedioate complexes of Mn(II) and Mn(III).

      • [Mn^II(H₂O)₆]²⁺_(aq) ==> [Mn^II(C₂O₄)₃]^4-_(aq)  ==>  [Mn^III(C₂O₄)₃]^3-_(aq) ==> [Mn(H₂O)₆]²⁺_(aq) + CO_2(aq/g) 

      • Note that the catalytic cycle involves changes in ligand and oxidation state in the manganese metal ions and two intermediate complexes.

    • (iii) Cobalt(II) ions catalyse the oxidation of the 2,3-dihydroxybutandioate ion (from acid/salt, old name '') to water, methanoate ion and carbon dioxide.

      • the pink hexaaqua Co²⁺ ion 

      • [Co(H₂O)₆]²⁺_(aq) ==> [Co(OOCCHOHCHOHCOO)₃]^4-_(aq)  == via H₂O_2(aq)= ===>

      • [Co(OOCCHOHCHOHCOO)₃]^3-_(aq) ==> [Co(H₂O)₆]²⁺_(aq) + H₂O_(l), HCOO^-_(aq), CO_2(aq/g) 

    • (iv)

• Transition metal ions at the 'heart' of many enzymes - biological catalysts or 'molecule carriers'

  • Examples to add

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 7. Balancing redox equations

1. use of the correct 'species' (e.g. usually two given/chosen as/from half-cell equation data)

2. the 'species' direction change - which is oxidised or reduced? (if not indicated, might have to decide from E^Ø data, the more +ve half-cell gets reduced)

3. correct ratio of half-cell equations - the 'balance' must be based on oxidation number analysis, the total increase in oxidation states must be equal to the total decrease in oxidation state

4. add up the ion charges, the totals should be the same on both sides of the equation (I find this a handy extra check especially with stray H⁺'s!)

5. 'traditional' atom count - placed last because its not completely reliable with redox equations!

6. There are two separate web pages with help and examples explained

   Revision notes on Inorganic redox reactions - Part 1 electronegativity, explaining oxidation and reduction reactions and oxidation state/oxidation number

   Revision notes on Inorganic redox reactions - Part 2 analysing and constructing full redox equations from half-cell reactions

Quick click to Introduction * Sc * Ti * V * Cr * Mn * Fe * Co * Ni * Cu * Zn * Ag/Pt etc.

10c Appendix 8. Complex ion stability, entropy changes and stability constants (K_stab)